For amny writers the hardest ways of characterization are through using narration, exposition and analysis. I have to agree. It's easy to show your character through action, through their speech both internal and external.
Narration is tell, so are exposition and analysis. We constantly hear show, don't tell but too much show can send the pace of the story into overdrive leaving the reader with no time to take a breath and to think about what the story is about.
The secret to good characterization is for the author to identify with the character, almost to become the character. Does this mean writers have split-personalities? Perhaps. The writer's belief in the character is what brings the reader into the story. They are the second part of what makes a character.
With all these ways of showing a character by using the tell move, there are several things to avoid. Giving a list of traits and telling too much. We've all read both and probably done them. Turn the lists into something else and only telling the reader what they need to know about a character. Those lists and all that information the writer needs but it doesn't need to go into the story, at least not in one huge gulp.
So how does one use these telling ways to show the character. Suggestive words and phrase. Choosing verbs and nouns that describe and have an impact. Tilly tensed and waited for the slam of the door. George always announced his departure with a final punctuation of his angry diatribe.
Pictorial writing is another way. This means using words to capture images. The senses can always add to a telling passage. Not just sight but all the senses, touch, smell, taste, and sound. Figures of speech are also good ways to tell readers about a character. There's contrast. A good thing is to evoke the reader's memory of images and sensations. Let the aromas of food tell the reader a bit about how the character enjoys the aroma of coffee, the taste of chocolate chip cookies. There are images and sensations that most people have experienced.
Do you use only action, dialogue and thoughts to show your characters? Take some time to explore other ways in an active rather than a passive way.